On the group of homeomorphisms on R: A revisit
Keywords:Group of homeomorphisms, Normal subgroups, Dynamical systems, Fixed points, Conjugacy, bounded functions
In this article, we prove that the group of all increasing homeomorphisms on R has exactly five normal subgroups, and the group of all homeomorphisms on R has exactly four normal subgroups. There are several results known about the group of homeomorphisms on R and about the group of increasing homeomorphisms on R (, ,  and ), but beyond this there is virtually nothing in the literature concerning the topological structure in the aspects of topological dynamics. In this paper, we analyze this structure in some detail.
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University of Calicut
Grant numbers U.O. No. 11733/2021/Admn